Chris UnsworthA Specialised Constraint approach for Stable Matching problems

The Stable marriage problem

There exists an optimal algorithmEGS runs in O(n2) time

There are optimal constraint encodingsBoolean encoding proposed CP’01

LimitationsEGS is highly specialisedCP encodings are slowRequire large supporting data structures

My contributionFast specialised constraints for SMSM2, SMN, BSMN, CSMNTheoretically and empirically testedProven to be sound and completeDemonstrated their versatility

The Hospital/Residents problem

Two linear time algorithms exist

The Resident-oriented and Hospital-oriented algorithms

Constraint models have been proposed

Constraint based encoding proposed at CPAIOR’07

My contribution

Fast specialised constraint for HRHRNTheoretically and empirically testedDemonstrated its versatility

Large scale empirical study

Compared all stable marriage constraint models

Over 20,000 randomly generated instances

Demonstrated Versatility

Eight variants of stable matching problems taken from the literatureOptimisation problems

– Sex-equal, balanced, egalitarian

Specialisations– Man-exchange, forced pairs, couples

Future directions

Optimisation problems

Variable and value ordering heuristics

Different search strategies

Ties and incomplete preference lists

How current constraint models can be adapted

How the problem can be reformulated

Higher levels of consistency

Enforcing GAC over SMNEmulating stable pairs algorithm